pastas.stats.metrics.aic
========================

.. py:function:: pastas.stats.metrics.aic(obs: pandas.Series | None = None, sim: pandas.Series | None = None, res: pandas.Series | None = None, missing: str = 'drop', nparam: int = 1) -> float

   
   Compute the Akaike Information Criterium (AIC).

   :param obs: Series with the observed values.
   :type obs: pandas.Series, optional
   :param sim: The Series with the simulated values.
   :type sim: pandas.Series, optional
   :param res: The Series with the residual values. If time series for the residuals
               are provided, the sim and obs arguments are ignored. Note that the
               residuals must be computed as `obs - sim` here.
   :type res: pandas.Series, optional
   :param nparam: number of calibrated parameters.
   :type nparam: int, optional
   :param missing: string with the rule to deal with missing values. Only "drop" is
                   supported now.
   :type missing: str, optional

   .. rubric:: Notes

   The Akaike Information Criterium (AIC) :cite:p:`akaike_new_1974` is computed as
   follows:

   .. math:: \text{AIC} = -2 log(L) + 2 nparam

   where :math:`n_{param}` is the number of calibration parameters and L is
   the likelihood function for the model. In the case of ordinary least
   squares:

   .. math:: log(L) = - (nobs / 2) * log(RSS / -nobs)

   where RSS denotes the residual sum of squares and nobs the number of
   observations.















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